μGUIDE: a framework for quantitative imaging via generalized uncertainty-driven inference using deep learning

Reviewer #1 (Public Review):

The authors proposed a framework to estimate the posterior distribution of parameters in biophysical models. The framework has two modules: the first MLP module is used to reduce data dimensionality and the second NPE module is used to approximate the desired posterior distribution. The results show that the MLP module can capture additional information compared to manually defined summary statistics. By using the NPE module, the repetitive evaluation of the forward model is avoided, thus making the framework computationally efficient. The results show the framework has promise in identifying degeneracy. This is an interesting work.

Reviewer #2 (Public Review):

Summary:
The authors improve the work of Jallais et al. (2022) by including a novel module capable of automatically learning feature selection from different acquisition protocols inside a supervised learning framework. Combining the module above with an estimation framework for estimating the posterior distribution of model parameters, they obtain rich probabilistic information (uncertainty and degeneracy) on the parameters in a reasonable computation time.

The main contributions of the work are:
(1) The whole framework allows the user to avoid manually defining summary statistics, which may be slow and tedious and affect the quality of the results.
(2) The authors tested the proposal by tackling three different biophysical models for brain tissue and using data with characteristics commonly used by the diffusion-MR-microstructure research community.
(3) The authors validated their method well with the state-of-the-art.

The main weakness is:
(1) The methodology was tested only on scenarios with a signal-to-noise ratio (SNR) equal to 50. It is interesting to show results with lower SNR and without noise that the method can detect the model's inherent degenerations and how the degeneration increases when strong noise is present. I suggest expanding the Figure in Appendix 1 to include this information.

The authors showed the utility of their proposal by computing complex parameter descriptors automatically in an achievable time for three different and relevant biophysical models.

Importantly, this proposal promotes tackling, analyzing, and considering the degenerated nature of the most used models in brain microstructure estimation.

Author response:

We appreciate the time and effort that you and the reviewers have dedicated to providing valuable feedback on our manuscript. We are grateful to the reviewers for their insightful comments.

Reviewer #1:
We thank the reviewer for the positive comments made on our manuscript.

Reviewer #2:
We thank the reviewer for these positive remarks.

Concerning the main weakness highlighted by the reviewer:

We presented results in our submitted work both without noise and with a signal-to-noise ratio (SNR) equal to 50. Figure 5 shows exemplar posterior distributions obtained in a noise-free scenario, and Table 1 reports the number of degeneracies for each model on 10000 noise-free simulations. These results highlight that the presence of degeneracies is inherent to the model definition. Figures 3, 6 and 7 present results considering an SNR of 50. Results with lower SNR have indeed not been included into this work. We agree that adding a figure showing the impact of noise on the posterior distributions will be a good addition to this work. We will include an additional figure in the second version, as interestingly suggested.